Question

12 O 44 Madeline, Tyra, and Imogen are helping consolidate leftover pizza slices after a party. Each one of them has a box with leftovers. Madeline says the leftover slices in her box form a 203° angle . Tyra says the leftover slices in her box form a 59 After hearing those descriptions from Madeline and Tyra, Imogen wonders if the leftover slices would all fit into one box (meaning one full circle of 360° or less). It is possible if the angle measure of her leftover slices is no larger than [Drop Down 1]. If each slice has an angle of 40 the maximum amount of slices Imogen can fit is [Drop Down 2]. 1 mron Down 11​

Answer 1

i. The angle measure of Imogen's leftover should not be larger than
`98^(o)`

ii. The maximum number of slices that Imogen can fit is 2.

Explanation:

The leftover in Madeline's box forms angle = 203°

The leftover in Tyra's box forms angel =
`59^(o)`

Sum of angles formed = 203° +
`59^(o)`

=
`262^(o)`

Given that one box = 1 full circle of 360°. Then,

the angle formed by the leftover in Imogen's box = 360° -
`262^(o)`

=
`98^(o)`

Thus, the angle measure of Imogen's leftover slices should not be larger than
`98^(o)`.

If each slice has an angle of
`40^(o)`, the maximum number of slice that Imogen can fit =
`(98)/(40)`

= 2
`(9)/(20)`

= 2.45

The maximum number of slices that Imogen can fit is 2.